System and method for reducing printable defects on extreme ultraviolet pattern masks

ABSTRACT

A system for reducing printable defects on a pattern mask is disclosed. The system includes a controller configured to be communicatively coupled to a characterization sub-system, the controller including one or more processors configured to execute program instructions causing the one or more processors to: direct the characterization sub-system to perform inspection of a mask blank; generate a cost function based on a first characteristic and a second characteristic, the first characteristic comprising areas of defect regions exposed by mask patterns, the second characteristic comprising pattern complexity of a design pattern; determine one or more values indicative of a minimum of the cost function via a non-linear optimization procedure; and generate one or more control signals to adjust rotation and translation of the mask blank relative to the design pattern based on the determined one or more values indicative of the minimum of the cost function.

CROSS-REFERENCE TO RELATED APPLICATION

The present application claims priority to U.S. Provisional ApplicationSer. No. 62/913,659, filed Oct. 10, 2019, entitled FAST METHOD FOREXTREME ULTRAVIOLET PHOTOMASK BLANK DEFECT OPTIMIZATION, naming XiaochunYang, Vikram Tolani, and Yao Zhang as inventors, which is incorporatedherein by reference in the entirety.

TECHNICAL FIELD

The present invention generally relates to pattern masks for use inlithography systems, and, more particularly, to a system and method forreducing printable defects on EUV pattern masks using a cost function.

BACKGROUND

Extreme ultraviolet lithography (EUVL) remains the leading technologyfor Next-Generation Lithography. However, one of the key challengesfacing EUVL is mask blank defectivity. EUV masks are Bragg reflectorsincluding several alternating layers of molybdenum and silicon. Thedesign pattern is placed on the top of this multilayer reflector in theform of an absorber layer. Mask blank defects formed during fabricationof the mask blanks significantly alter the design pattern printed on themask blank that is later transferred onto the sample during EUVL.Repairing these defects is challenging because the defects are buriedunder the multilayers of the EUV mask blank. Implementation of EUVL forhigh volume manufacture requires the semiconductor industry to overcomethese challenges, however, there currently are no feasible solutionsavailable to produce defect-free mask blanks and no cost-effective toolsto repair the buried defects. Therefore, it would be desirable toprovide a system and method that cure the shortfalls of the previousapproaches identified above.

SUMMARY

A system for reducing printable defects on a pattern mask is disclosed,in accordance with one or more embodiments of the present disclosure. Inone embodiment, the system includes a controller configured to becommunicatively coupled to a characterization sub-system, the controllerincluding one or more processors configured to execute programinstructions causing the one or more processors to: direct thecharacterization sub-system to perform inspection of a mask blank togenerate a defect map of one or more defects in the mask blank; generatea cost function based on a first characteristic and a secondcharacteristic, the first characteristic comprising an area of defectexposure of the one or more defects on the mask blank, the secondcharacteristic comprising pattern complexity of a design pattern withina defect region; determine one or more values indicative of a minimum ofthe cost function via a non-linear optimization procedure; and generateone or more control signals to adjust rotation and translation of themask blank relative to the design pattern based on the determined one ormore values indicative of the minimum of the cost function.

A system for reducing printable defects on a pattern mask is disclosed,in accordance with one or more embodiments of the present disclosure. Inone embodiment, the system includes a controller configured to becommunicatively coupled to a characterization sub-system, the controllerincluding one or more processors configured to execute programinstructions causing the one or more processors to: direct thecharacterization sub-system to perform inspection of a mask blank togenerate a defect map of one or more defects in the mask blank; generatea cost function based on a first characteristic and a secondcharacteristic, the first characteristic comprising an area of defectexposure of the one or more defects on the mask blank, the secondcharacteristic comprising pattern complexity of a design pattern withina defect region; determine one or more values indicative of a minimum ofthe cost function via a non-linear optimization procedure; determine oneor more metrics indicative of how good the mask blank is for the designpattern; and generate one or more control signals to adjust rotation andtranslation of the mask blank relative to the design pattern based on atleast one of the determined one or more values indicative of the minimumof the cost function or the one or more metrics indicative of how goodthe mask blank is for the design pattern.

A method for reducing printable defects on a pattern mask is disclosed,in accordance with one or more embodiments of the present disclosure. Inone embodiment, the method includes directing a characterizationsub-system to perform inspection of a mask blank to generate a defectmap of one or more defects in the mask blank. In another embodiment, themethod includes generating a cost function based on a firstcharacteristic and a second characteristic, the first characteristiccomprising an area of defect exposure of the one or more defects on themask blank, the second characteristic comprising pattern complexity of adesign pattern within a defect region. In another embodiment, the methodincludes determining one or more values indicative of a minimum of thecost function via a non-linear optimization procedure. In anotherembodiment, the method includes generating one or more control signalsto adjust rotation and translation of the mask blank relative to thedesign pattern based on the determined one or more values indicative ofthe minimum of the cost function.

A method for reducing printable defects on a pattern mask is disclosed,in accordance with one or more embodiments of the present disclosure. Inone embodiment, the method includes directing a characterizationsub-system to perform inspection of a mask blank to generate a defectmap of one or more defects in the mask blank. In another embodiment, themethod includes generating a cost function based on a firstcharacteristic and a second characteristic, the first characteristiccomprising an area of defect exposure of the one or more defects on themask blank, the second characteristic comprising pattern complexity of adesign pattern within a defect region. In another embodiment, the methodincludes determining one or more values indicative of a minimum of thecost function via a non-linear optimization procedure. In anotherembodiment, the method includes determining one or more metricsindicative of how good the mask blank is for the design pattern. Inanother embodiment, the method includes generating one or more controlsignals to adjust rotation and translation of the mask blank relative tothe design pattern based on at least one of the determined one or morevalues indicative of the minimum of the cost function or the one or moremetrics indicative of how good the mask blank is for the design pattern.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not necessarily restrictive of the invention as claimed. Theaccompanying drawings, which are incorporated in and constitute a partof the specification, illustrate embodiments of the invention andtogether with the general description, serve to explain the principlesof the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The numerous advantages of the disclosure may be better understood bythose skilled in the art by reference to the accompanying figures inwhich:

FIG. 1A is a conceptual view illustrating a system for reducingprintable defects in pattern masks, in accordance with one or moreembodiments of the present disclosure.

FIG. 1B is a conceptual view illustrating an extreme ultravioletlithography sub-system, in accordance with one or more embodiments ofthe present disclosure.

FIG. 1C is a conceptual view illustrating a characterization sub-system,in accordance with one or more embodiments of the present disclosure.

FIG. 2A is a conceptual view illustrating a mask blank withimperfections before a design pattern is printed onto the mask blank, inaccordance with one or more embodiments of the present disclosure.

FIG. 2B is a conceptual view illustrating a pattern mask withimperfections after the design pattern has been printed onto the maskblank, in accordance with one or more embodiments of the presentdisclosure.

FIG. 3A is a conceptual view illustrating the impact of a transferredmask blank defect on a design pattern of a sample, in accordance withone or more embodiments of the present disclosure.

FIG. 3B is a conceptual view illustrating the impact of a transferredmask blank defect on a design pattern of a sample, in accordance withone or more embodiments of the present disclosure.

FIG. 4 is a conceptual flow diagram of a method for reducing printabledefects in pattern masks, in accordance with one or more embodiments ofthe present disclosure.

FIG. 5 is a conceptual view illustrating an example of mask blankshifting, in accordance with one or more embodiments of the presentdisclosure.

FIG. 6 is a conceptual view illustrating an example of a design patternshift suggestion based on the cost function, in accordance with one ormore embodiments of the present disclosure.

FIG. 7A is a conceptual view illustrating pattern complexity, inaccordance with one or more embodiments of the present disclosure.

FIG. 7B is a conceptual view illustrating pattern complexity, inaccordance with one or more embodiments of the present disclosure.

FIG. 8 is a conceptual view illustrating the adding a margin to the maskblank defect, in accordance with one or more embodiments of the presentdisclosure.

FIG. 9 illustrates a flow chart of a method for reducing printabledefects in pattern masks using a cost function, in accordance with oneor more embodiments of the present disclosure.

FIG. 10 illustrates a flow chart of a method for reducing printabledefects in pattern masks using a cost function, in accordance with oneor more embodiments of the present disclosure.

DETAILED DESCRIPTION

The present disclosure has been particularly shown and described withrespect to certain embodiments and specific features thereof. Theembodiments set forth herein are taken to be illustrative rather thanlimiting. It should be readily apparent to those of ordinary skill inthe art that various changes and modifications in form and detail may bemade without departing from the spirit and scope of the disclosure.

Reference will now be made in detail to the subject matter disclosed,which is illustrated in the accompanying drawings.

EUVL remains the leading technology for Next-Generation Lithography.However, one of the key challenges facing this technology is mask blankdefectivity. Currently, there are no feasible solutions available toproduce defect-free mask blanks and no cost-effective tools to repairthe defects on the mask blanks. Thus, the ability to tolerate some ofthese defects without any impacts on yield is crucial. Defect avoidanceand mitigation techniques have emerged as a highly effective approach toincrease the tolerance of mask defects. Current mask defectmitigation/avoidance methods use the distance between a defect and anabsorber edge to compute the impact of the defect on pattern criticaldimension, which is not sufficient. Such methods fail to considerextended affected region of defects on complex-pattern areas. Aprohibited-shift-rectangle/prohibited-relocation-cube (PSR/PRC) is thencomputed to find a point that minimizes the number of overlappedPSR/PRC. Alternatively, another approach currently used is to develop anoptical model configured to solve a non-convex optimization problem bygradient descend.

Embodiments of the present disclosure are directed to a system andmethod for reducing printable defects on EUV photomasks, in accordancewith one or more embodiments of the present disclosure. Specifically,embodiments of the present disclosure are directed to using a costfunction based on the exposure region of defects and pattern complexity,such that the cost function may be configured to mitigate printable maskdefects in EUV photomasks used in EUVL. The cost function may beminimized using a fast-non-linear optimization procedure to estimate aset of parameters (e.g., rotation and translation) to optimally hide theone or more defects in the absorber layer. The cost function may beconfigured to provide one or more defect hiding solutions for EUV maskmanufacturing to minimize the impact of mask blank defects to a waferwithin a reasonable process time. For example, the system may beconfigured to suggest a hiding solution such that the mask blank defectsare hidden by the absorber layer of the photomask with minimized defectimpact on pattern printability. A hidden blank defect (rather than anexposed defect) is less printable in the sample, so its adverse impacton pattern critical dimension is tolerable during fabrication. Further,defect mitigation reduces the wastage of EUV blanks, which are veryexpensive to produce, thereby improving yielding.

Referring generally to FIGS. 1A-10, a system and method for reducingprintable defects on EUV pattern masks using a cost function isdescribed, in accordance with one or more embodiments of the presentdisclosure.

FIG. 1A is a conceptual view illustrating a system 100 for reducingprintable defects on EUV pattern masks using a cost function, inaccordance with one or more embodiments of the present disclosure. Inone embodiment, the system 100 includes an extreme ultraviolet (EUV)lithography sub-system 102 for lithographically printing one or morepatterns to a sample 128. The EUV lithography sub-system 102 may includeany lithographic printing tool known in the art. For example, the EUVlithography sub-system 102 may include, but is not limited to, a scanneror stepper. The EUV lithography sub-system 102 may operate byilluminating a pattern mask, which then reflects the illuminationaccording to the mask elements on the pattern mask. Optical elementswithin the lithography system (e.g., a set of projection optics) maythen generate an image of the pattern mask on the sample based on thereflected illumination from the pattern mask collected by the set ofprojection optics.

In another embodiment, the system 100 includes one or more pattern maskfabrication sub-systems 104 for fabricating pattern masks for use in theEUV lithography sub-system 102. The one or more pattern mask fabricationsub-systems 104 may include any fabrication tool known in the artsuitable for pattern mask fabrication. For example, the one or morepattern mask fabrication sub-systems 104 may include, but are notlimited to, one or more deposition tools, one or more metrology tools,or the like. The one or more pattern mask fabrication sub-systems 104may be configured to fabricate any type of pattern mask known in the artincluding, but not limited to, an extreme ultraviolet pattern mask. TheEUV pattern mask may include at least one of a multilayer reflectorportion, a capping layer, and an absorber layer. For example, the one ormore pattern mask fabrication sub-systems 104 may be configured togenerate an EUV pattern mask with an adjusted design pattern based on acost function, as discussed further herein with respect to FIGS. 4-10.

In another embodiment, the system 100 includes a characterizationsub-system 106 configured to perform defect inspection in a layer of amask blank 500 (shown in FIG. 5). It is noted herein that thecharacterization sub-system 106 may include, but is not limited to, aninspection sub-system or a metrology sub-system. The characterizationsub-system 106 may include any inspection sub-system 106 known in theart including, but not limited to, an optical-based inspection tool, acharged particle-based inspection tool, a review tool, and the like. Thecharacterization sub-system 106 may include any imaging-based metrologysub-system 106 known in the art including, but not limited to, anoptical imaging-based metrology tool, a scanning electron microscopy(SEM) tool, or the like.

In another embodiment, the system 100 includes a controller 108. Inanother embodiment, the controller 108 includes one or more processors110 configured to execute program instructions maintained on a memorymedium 112. In this regard, the one or more processors 110 of controller108 may execute any of the various process steps described throughoutthe present disclosure. Further, the controller 108 may becommunicatively coupled to the mask support device 124 and/or the samplestage 130 to direct the transfer of pattern elements on a pattern mask122 to a sample 128. It is noted herein that the EUV lithographysub-system 102 of the present invention may implement any of the patternmask designs described throughout the present disclosure.

The characterization sub-system 106 may provide various types ofcharacterization data related to the layers of the mask blank. Forexample, the characterization sub-system 106 may provide defectcharacterization data. For instance, the characterization sub-system 106may provide the location, size, number, or type of defect in the maskblank layers.

FIG. 1B is a conceptual view illustrating the EUV lithography sub-system102, in accordance with one or more embodiments of the presentdisclosure. In one embodiment, the EUV lithography sub-system 102includes an illumination source 114 configured to generate one or moreillumination beams 116. The illumination beam 116 may include one ormore selected wavelengths of EUV light. For example, at least a portionof a spectrum of the illumination beam 116 may include wavelengthsassociated with a EUV-based lithography device suitable forsemiconductor fabrication such as, but not limited to, 13.5 nm, or thelike. EUV-based lithography is described generally in U.S. Pat. No.8,916,831 to Wang, issued on Dec. 23, 2014, which is incorporated hereinby reference in the entirety.

In one embodiment, the illumination source 114 includes an extremeultraviolet illumination source 114. For example, the EUV illuminationsource 114 may include a broadband plasma (BBP) illumination source. Inthis regard, the illumination beam 116 may include radiation emitted bya plasma. For example, a BBP illumination source 114 may include, but isnot required to include, one or more pump sources (e.g., one or morelasers) configured to focus illumination into the volume of a gas,causing energy to be absorbed by the gas in order to generate or sustaina plasma suitable for emitting radiation. Further, at least a portion ofthe plasma radiation may be utilized as the illumination beam 116. Inanother embodiment, the illumination source 114 may include one or morelasers capable of emitting radiation at one or more selectedwavelengths.

In another embodiment, the illumination source 114 directs theillumination beam 116 to a pattern mask 122 via an illumination pathway118. The illumination pathway 118 may include one or more illuminationoptics 120 suitable for directing, focusing, and/or shaping theillumination beam 116 on the pattern mask 122. For example, theillumination optics 120 may include one or more lenses, one or morefocusing elements, or the like. Further, the illumination optics 120 mayinclude any reflective optical element known in the art suitable fordirecting and/or focusing the illumination beam 116. For instance, theillumination optics 120 may include reflective optics suitable fordirecting and/or focusing low-wavelength light (e.g., EUV light, and thelike) such as, but not limited to, flat mirrors or curved mirrors (e.g.,elliptical mirrors, parabolic mirrors, or the like).

The illumination optics 120 may further include one or more additionalillumination pathway components suitable for shaping the illuminationbeam 116 and/or controlling a range of incidence angles of theillumination beam 116 on the mask 122 (e.g., an illumination pupildistribution). For example, the illumination pathway components mayinclude, but are not limited to, one or more apertures, one or moreapodizers, one or more homogenizers, one or more diffusers, one or morepolarizers, or one or more filters.

In another embodiment, the EUV lithography sub-system 102 includes amask support device 124. The mask support device 124 may be configuredto secure the mask 122.

In another embodiment, the EUV lithography sub-system 102 includes a setof projection optics 126 configured to project an image of the patternmask 122 illuminated by the one or more illumination beams 116 onto thesurface of a sample 128 disposed on a sample stage 130. For example, theset of projection optics 126 may be configured to project an image ofthe pattern mask 122 onto a resist layer on the sample 128 to generate(e.g., expose, or the like) a printed pattern element on the resistlayer corresponding to a pattern element on the pattern mask 122. Inanother embodiment, the mask support device 124 may be configured toactuate or position the pattern mask 122. For example, the mask supportdevice 124 may actuate the pattern mask 122 to a selected position withrespect to the projection optics 126 of the EUV lithography sub-system102.

The pattern mask 122 may be utilized (e.g., by EUV lithographysub-system 102) in any imaging configuration known in the art. Forexample, the pattern mask 122 may be a positive mask (e.g., abright-field mask) in which pattern elements are positively imaged asprinted pattern elements of a resist layer of sample 128. By way ofanother example, the pattern mask 122 may be a negative mask (e.g., adark-field mask) in which pattern elements of the pattern mask 122 formnegative printed pattern elements (e.g., gaps, spaces, or the like) of aresist layer of sample 128.

As used throughout the present disclosure, the term “sample” generallyrefers to a substrate formed of a semiconductor or non-semiconductormaterial (e.g., a wafer, or the like). For example, a semiconductor ornon-semiconductor material may include, but is not limited to,monocrystalline silicon, gallium arsenide, and indium phosphide. Asample may include one or more layers. For example, such layers mayinclude, but are not limited to, a resist, a dielectric material, aconductive material, and a semiconductive material. Many different typesof such layers are known in the art, and the term sample as used hereinis intended to encompass a sample on which all types of such layers maybe formed. One or more layers formed on a sample may be patterned orunpatterned. For example, a sample may include a plurality of dies, eachhaving repeatable patterned features. Formation and processing of suchlayers of material may ultimately result in completed devices. Manydifferent types of devices may be formed on a sample, and the termsample as used herein is intended to encompass a sample on which anytype of device known in the art is being fabricated. Further, for thepurposes of the present disclosure, the term sample and wafer should beinterpreted as interchangeable. In addition, for the purposes of thepresent disclosure, the terms patterning device, pattern mask, mask, andreticle, should be interpreted as interchangeable.

FIG. 1C is a conceptual view illustrating the characterizationsub-system 106, in accordance with one or more embodiments of thepresent disclosure. In one embodiment, the characterization sub-system106 includes an illumination source 140 to generate an illumination beam142. The illumination beam 142 may include one or more selectedwavelengths of light including, but not limited to, ultraviolet (UV)radiation, visible radiation, or infrared (IR) radiation. It is notedherein that the characterization sub-system 106 may include any type ofcharacterization sub-system 106 known in the art without limiting thescope of the present disclosure. For example, although not depicted inFIG. 1C, the characterization sub-system 106 may include an extremeultra violet (EUV) characterization sub-system, a deep ultraviolet (DUV)characterization sub-system, or the like without departing from thescope of the present disclosure.

In another embodiment, the illumination source 140 directs theillumination beam 142 to the sample 128 via an illumination pathway 144.The illumination pathway 144 may include one or more lenses 146.Further, the illumination pathway 144 may include one or more additionaloptical components 148 suitable for modifying and/or conditioning theillumination beam 142. For example, the one or more optical components148 may include, but are not limited to, one or more polarizers, one ormore filters, one or more beam splitters, one or more diffusers, one ormore homogenizers, one or more apodizers, or one or more beam shapers.In one embodiment, the illumination pathway 144 includes a beamsplitter150. In another embodiment, the characterization sub-system 106 includesan objective lens 152 to focus the illumination beam 142 onto the sample128.

In another embodiment, the characterization sub-system 106 includes oneor more detectors 154 configured to capture radiation emanating from thesample 128 through a collection pathway 156. The collection pathway 156may include multiple optical elements to direct and/or modifyillumination collected by the objective lens 152 including, but notlimited to one or more lenses 146, one or more filters, one or morepolarizers, one or more beam blocks, or one or more beamsplitters.

For example, a detector 154 may receive an image of the sample 128provided by elements in the collection pathway 156 (e.g., the objectivelens 152, the one or more lenses 146, or the like). By way of anotherexample, a detector 154 may receive radiation reflected or scattered(e.g., via specular reflection, diffuse reflection, and the like) fromthe sample 128. By way of another example, a detector 154 may receiveradiation generated by the sample (e.g., luminescence associated withabsorption of the illumination beam 142, and the like). Further, it isnoted herein that the one or more detectors 154 may include any opticaldetector known in the art suitable for measuring illumination receivedfrom the sample 128. For example, a detector 154 may include, but is notlimited to, a CCD detector, a TDI detector, a photomultiplier tube(PMT), an avalanche photodiode (APD), or the like.

In another embodiment, the characterization sub-system 106 iscommunicatively coupled to the controller 108 of system 100. In thisregard, the controller 108 may be configured to receive characterizationdata such as, but not limited to, defect characterization data.

The one or more processors 110 of a controller 108 may include anyprocessor or processing element known in the art. For the purposes ofthe present disclosure, the term “processor” or “processing element” maybe broadly defined to encompass any device having one or more processingor logic elements (e.g., one or more micro-processor devices, one ormore application specific integrated circuit (ASIC) devices, one or morefield programmable gate arrays (FPGAs), or one or more digital signalprocessors (DSPs)). In this sense, the one or more processors 110 mayinclude any device configured to execute algorithms and/or instructions(e.g., program instructions stored in memory). In one embodiment, theone or more processors 110 may be embodied as a desktop computer,mainframe computer system, workstation, image computer, parallelprocessor, networked computer, or any other computer system configuredto execute a program configured to operate or operate in conjunctionwith the system 100, as described throughout the present disclosure.

Moreover, different sub-systems of the system 100, such as thesub-systems 102, 104, 106 of system 100, may include a processor orlogic elements suitable for carrying out at least a portion of the stepsdescribed in the present disclosure. Therefore, the above descriptionshould not be interpreted as a limitation on the embodiments of thepresent disclosure but merely as an illustration. Further, the stepsdescribed throughout the present disclosure may be carried out by asingle controller 108 or, alternatively, multiple controllers.Additionally, the controller 108 may include one or more controllershoused in a common housing or within multiple housings. In this way, anycontroller or combination of controllers may be separately packaged as amodule suitable for integration into system 100.

The memory medium 112 may include any storage medium known in the artsuitable for storing program instructions executable by the associatedone or more processors 110. For example, the memory medium 112 mayinclude a non-transitory memory medium. By way of another example, thememory medium 112 may include, but is not limited to, a read-only memory(ROM), a random-access memory (RAM), a magnetic or optical memory device(e.g., disk), a magnetic tape, a solid-state drive and the like. It isfurther noted that memory medium 112 may be housed in a commoncontroller housing with the one or more processors 110. In oneembodiment, the memory medium 112 may be located remotely with respectto the physical location of the one or more processors 110 andcontroller 108. For instance, the one or more processors 110 ofcontroller 108 may access a remote memory (e.g., server), accessiblethrough a network (e.g., internet, intranet and the like).

FIGS. 2A-2B illustrate a comparison of pre-pattern and post-patternimperfections. In one embodiment, one or more defects 202 (orimperfections 202) in the mask blank 200 manifest as one or more defectson the pattern mask 206 after mask fabrication. These defects can beprintable after lithography and significantly impact the patterntransferred to the sample. For example, defects 208 may overlap withportions of the exposure region of a design pattern, while other defects204 may not overlap with the exposure region of the design pattern. Thedefects 208 that overlap with the exposure region of a pattern maysignificantly impact the pattern that is transferred to the sampleduring lithography.

FIGS. 3A-3B illustrate the impact of a transferred blank defect on thedesign pattern of a sample. As previously discussed herein, one keychallenge with EUVL is EUV mask blank defectivity. EUV masks are Braggreflectors including several alternating layers of molybdenum andsilicon. A design pattern is placed on the top of this multilayerreflector in the form of an absorber layer. Mask blank defects areformed during fabrication of the blanks. Mask blank defects formedduring fabrication of the masks significantly alters the design patternprinted on the sample. FIG. 3A depicts a sample pattern where the maskblank 300 is defect-free and FIG. 3B depicts a sample pattern where themask blank 304 includes a buried particle defect 306 in the multilayerportion 302 of the mask blank 304. As shown in FIG. 3B, this buriedparticle defect 306 impacts the design pattern transferred to thesample. For example, as shown in FIG. 3B, the buried particle defect 308is transferred to the sample and creates a similar defect 308 in thesample pattern. Repairing these defects is very challenging because thedefects are buried under multilayers.

FIG. 4 is a conceptual flow diagram of a method 400 for reducingprintable defects in EUV pattern masks, in accordance with one or moreembodiments of the present disclosure. It is noted herein that the stepsof method 400 may be implemented all or in part by system 100. It isfurther recognized, however, that the method 400 is not limited to thesystem 100 in that additional or alternative system-level embodimentsmay carry out all or part of the steps of method 400.

In one embodiment, the system 100 is configured to performpre-patterning inspection of a mask blank 500 (step 402). For example,the system 100 may be configured to direct the characterizationsub-system 106 to inspect a layer of the mask blank 500. For instance,the characterization sub-system 106 may be configured to generate adefect map (as shown by FIG. 5) of a layer of the mask blank 500including the location, size, number, and type of the one or moredefects 502 in the layers of the mask blank 500. In this regard, themask blank 500 may be adjusted (rotated and/or translated) to avoidplacing the design pattern 504 on the one or more defects 502 on themask blank 500 (as shown by 510). A bad solution is shown in 508 wherethe design pattern 504 touches a portion of the one or more defects 502.

In another embodiment, the controller 108 of the system 100 isconfigured to generate a cost function (step 404), with rotation andtranslation as parameters, based on a first characteristic and a secondcharacteristic of mask fabrication. For example, the cost function maybe based on an area of defect exposure and pattern complexity. Forinstance, the cost function may be based on a first characteristicincluding an exposed area of defect (such as the mask 122 shown in FIGS.1B-1C). In another instance, the cost function may be based on a secondcharacteristic including the pattern complexity of a design patternwithin a defect region. It is noted herein that the generated costfunction may be configured to avoid high priority defects, hide defectsby an absorber layer, and avoid defects on patterns of high complexity.

The cost function may be shown and described by Equation 1 (Eqn. 1):Cost_(θ)(Δx,Δy)=Σ_(i) W _(i)(W _(A)Area(D _(θ,i)(Δx,Δy)∩P)+W_(C)Complexity(D _(θ,i)(Δx,Δy)∩P))  Eqn. 1where θ is the angle to rotate the defective mask blank 500 around theblank center. In one embodiment, the system 100 is configured to supportrotation around the blank center in 90-degree increments. For example,the system 100 may be configured to support a rotation of 0°, 90°, 180°,270°, or the like around the blank center. It is noted herein that thelimit on the angle of rotation may be determined by mask writers. Thetranslation (or shift) of the mask blank 500 relative to the designpattern in the x- and y-direction is represented by Δx, Δy,respectively. It is noted herein that the result of mask blank rotationand/or translation may be included in the output parameters of asuggested solution after the one or more values indicative of a minimumof the cost function are determined (e.g., step 406).

The region of defect under mask rotation and translation is representedby D_(θ,i)(Δx, Δy). The intersect operation is represented by operator∩, and mask patterns are represented by P. As a result, D_(θ,i)(Δx,Δy)∩P represents the exposed area of the defect i with blank rotationand translation as parameters and determined by the mask pattern P,which is represented by polygons (or images).

W_(A) and W_(C) are the weights of the exposed area and patterncomplexity above the defect, respectively. The weights of eachcharacteristic controls which characteristic is more important than theother characteristic. For example, a higher weight for defect exposureindicates that hiding the defect under the absorber layer is morecritical than placing defects on a complex pattern. By way of anotherexample, a higher weight for pattern complexity indicates that avoidingdefects on a pattern of high complexity is more critical than defectexposure. It is noted herein that pattern complexity is often morecritical because defects on high complexity patterns have a greaterimpact on pattern critical dimension (CD).

In one embodiment, the pattern complexity (Complexity(D_(θ,i)(Δx,Δy)∩P)) is determined by critical dimension (CD) of patterns in thedefect region and density of small-CD patterns within the defect region.For example, as shown in FIGS. 7A-7B, the smaller the pattern CD thehigher density of such patterns and thus, the higher its patterncomplexity is.

In one embodiment, the area of exposure of a defect (Area(D_(θ,i)(Δx,Δy)∩P)) under blank rotation and translation is determined by the partof the defect that is not covered by the absorber layer. For example,the area of defect exposure may be determined using an accumulatedoverlapping area of one or more defect regions and exposure regions of adesign pattern. Area(D_(θ,i)(Δx, Δy)∩P) represents a function thatcomputes the ratio of the exposed area of a defect with mask patternscompared to the total defect area. For example, Area(D_(θ,i)(Δx, Δy)∩P)may equal 1.0, such that there is full overlap between the defectregions and the exposure regions of mask patterns (e.g., 100 percentexposure). By way of another example, Area(D_(θ,j)(Δx, Δy)∩P) may equal0.0, such that the defect is totally covered by absorber (e.g., zeropercent exposure).

W_(i) represents defect priority based on defect class or type. It isnoted herein that some defects are relatively easier to repair. Further,some defects do not affect wafer CD negatively as much as others. Inthis regard, these defects will be given a lower weight than defectsthat are difficult to repair (such as buried defects in blankmultilayers) or that are more critical to wafer CD. Those defects thatare difficult to repair or that are more critical to wafer CD will begiven a higher weight to ensure that such defects are maximally hiddenby the absorber layer and avoid design patterns of high complexity.

In another embodiment, the system 100 is configured to determine one ormore values indicative of a minimum of the cost function using anon-linear optimization procedure (step 406). For example, thecontroller 108 of the system 100 may be configured to determine the oneor more values indicative of the minimum of the cost function usingEquation 2 (Eqn. 2). For instance, Eqn. 2 may be configured to determinethe optimal parameters of the cost function (e.g., rotation andtranslation). In this regard, the minimum of the cost function may beconfigured to suggest to a user an angle to rotate the mask blank.Further, the minimum of the cost function may be configured to suggestto a user an amount to translate (shift) the mask blank in the x- andy-direction (as shown in FIGS. 5-6). For example, the mask blank 500 maybe rotated 270 degrees such that the one or more defects 502 do notimpact the design pattern 504.

Eqn. 2 is shown and described by:

$\begin{matrix}{\theta,{\left( {{\Delta\; x},{\Delta\; y}} \right) = {{\arg\min}_{\theta,{({{\Delta\; x},{\Delta\; y}})}}\begin{Bmatrix}{{Cost}_{\theta = {0{^\circ}}}\left( {{\Delta\; x},{\Delta\; y}} \right)} \\{{Cost}_{\theta = {90{^\circ}}}\left( {{\Delta\; x},{\Delta\; y}} \right)} \\{{Cost}_{\theta = {180{^\circ}}}\left( {{\Delta\; x},{\Delta\; y}} \right)} \\{{Cost}_{\theta = {270{^\circ}}}\left( {{\Delta\; x},{\Delta\; y}} \right)}\end{Bmatrix}}}} & {{Eqn}.\mspace{14mu} 2}\end{matrix}$

In one embodiment, the system 100 utilizes the minimum of the costfunction (Eqn. 2) to determine an optimal discrete rotation angle andshift amount such that defects are hidden by an absorber layer, as shownin FIG. 6. In another embodiment, the system 100 utilizes the minimum ofthe cost function to determine an optimal discrete rotation angle andshift amount such that defects on high complexity patterns are avoided,as shown in FIGS. 7A-7B.

FIG. 6 is a conceptual view illustrating an example of mask blankshifting, in accordance with one or more embodiments of the presentdisclosure. In one embodiment, the system 100 is configured to adjustthe rotation and translation of the mask blank based on the minimum ofthe cost function determined in step 406. For example, as shown in FIG.6, the rotation and translation of the mask blank may be adjusted suchthat the defects are hidden by the absorber layer 602 of the mask 600.For instance, a defect 606 a located in the exposure region 604 may behidden under the absorber layer 602 (as indicated by the defect 606 b)by adjusting the rotation and translation of the mask blank. In anotherinstance, a defect 608 a located in the exposure region 604 may behidden under the absorber layer 602 (as indicated by the defect 608 b)by adjusting the rotation and translation of the mask blank. Theoptimization result provides the solution of mask blank translation androtation compared to the original pattern layer design.

In some embodiments, the system 100 is configured to generate one ormore metrics indicative of how good the adjusted mask blank is for thedesign pattern. For example, the controller 108 of the system 100 may beconfigured to generate one or more metrics indicative of how good themask blank is for the design pattern (step 408). The one or more metricsindicative of how good the mask blank is for a specified pattern isshown and described by Equations 3-4 (Eqn. 3-4):

$\begin{matrix}{\mspace{79mu}{{{score}_{\theta}\left( {{\Delta\; x},{\Delta\; y}} \right)} = \frac{\sum\limits_{i}{{metrics}\left( {D_{\theta,i}\left( {{\Delta\; x},{\Delta\; y}} \right)} \right)}}{N}}} & {{Eqn}.\mspace{14mu} 3} \\{{metrics}\left( {{D_{\theta,i}\left( {{\Delta x},{\Delta y}} \right)} = e^{{- \frac{10}{\max{({W_{A},W_{C}})}}}{({{W_{A}{{Area}{({{D_{\theta,i}{({{\Delta\; x},{\Delta\; y}})}}\bigcap P})}}} + {W_{C}{{Complexity}{({{D_{\theta,i}{({{\Delta\; x},{\Delta\; y}})}}\bigcap P})}}}}}}} \right)} & {{Eqn}.\mspace{14mu} 4}\end{matrix}$where N is the total number of defects. In one embodiment, the one ormore metrics includes a score between 0 and 1. For example, thecontroller 108 of the system 100 may be configured to determine a scorebetween 0 and 1 using Eqns. 3-4. A score closer to 1 indicates that themask blank is a good match for the specified design pattern P. The scoregives a user an intuitive indication of how good the blank is for themask pattern P. It is noted herein that this score may be used by a userto select the best suitable mask blank from a mask library for a givenmask pattern P. For example, the best mask blank from a mask blanklibrary may be selected so that all mask blanks are best utilized. Thus,it can maximally reduce blank wastage and greatly improve the yield inproduction environment.

In one embodiment, the system 100 is configured to generate one or morecontrol signals to adjust the rotation and translation of the mask blankrelative to a design pattern (step 410). For example, the one or morecontrol signals may be generated based on the minimum of the costfunction. For instance, the minimum of the cost function may include anoptimal rotation and translation amount such that the defects will behidden by an absorber layer when the design pattern is written on themask blank.

In some embodiments, the one or more pattern mask fabricationsub-systems 104 of the system 100 may be configured to print theadjusted design pattern on the mask blank 500 to generate the EUV mask(such as the mask 122 shown in FIGS. 1B-1C) (step 412). For instance,the one or more pattern mask fabrication sub-systems 104 may beconfigured to print the adjusted pattern on the mask blank such that theone or more defects on the mask blank are hidden by an absorber layer ofthe mask blank. In this regard, the one or more blank defects are hiddensuch that they do not significantly impact the pattern transferred tothe sample.

It is noted herein that utilizing the cost function shown and describedby Eqn. 1 allows for a user to perform blank defect optimization withina reasonable amount of time. For example, for approximately 120 defects,the runtime of the system 100 may be approximately 1 minute and 33seconds. By way of another example, for approximately 1000 defects, theruntime of the system 100 may be approximately 30 minutes.

It is noted herein that it may be desirable to position defects a selectdistance away from an absorber edge, since even defects hidden by anabsorber layer may be exposed if they are too close to the absorberedge. Further, such defects may also affect wafer CD. In someembodiments, as shown in FIG. 8, the defects may be extended by adding amargin 800 to defect size in the cost function. For example, during costfunction optimization (step 406), the optimizer may shift the mask blankmore than it would otherwise be shifted (e.g., as shown by 806 b and 806c in FIG. 8), such that defects are positioned a select distance awayfrom absorber edge 808. For instance, the optimizer may shift the maskblank such that the defect 806 a is positioned at point 806 b, ratherthan at position 806 c, such that the defect is positioned further awayfrom the absorber edge 808.

In some embodiments, the system 100 is configured to perform EUVlithography (EUVL) (step 414) using the EUV mask generated in step 412.For example, the EUV lithography sub-system 102 may be configured toperform EUV lithography using the EUV mask to transfer the designpattern on the EUV mask to the sample 128.

In an additional/alternative embodiment, pattern complexity may becalculated from one or more simulated aerial images. For example, anaerial image may be obtained from a design pattern by forwardlithography simulation. In this regard, pattern complexity then may becomputed through log slope of the simulated aerial image.

FIG. 9 illustrates a flowchart of a method 900 for reducing printabledefects in EUV photomasks using a cost function, in accordance with oneor more embodiments of the present disclosure. It is noted herein thatthe steps of method 900 may be implemented all or in part by system 100.It is further recognized, however, that the method 900 is not limited tothe system 100 in that additional or alternative system-levelembodiments may carry out all or part of the steps of method 900.

In step 902, blank inspection of the mask blank 500 is performed togenerate a defect map. In one embodiment, the system 100 is configuredto direct the characterization sub-system 106 to perform pre-patterninspection of the mask blank to generate a defect map of layers of themask blank 500. For example, the characterization sub-system 106 may beconfigured to identify the number, size, type, and location of one ormore defects 502 in the mask blank 500.

In step 904, a cost function is generated with rotation and translationas parameters. In one embodiment, the controller 108 of the system 100is configured to generate a cost function based on a firstcharacteristic and a second characteristic of the cost function (such asthe cost function shown in Eqn. 1) with rotation and translation asparameters of the cost function. For example, the first characteristicof the cost function may include an exposed area of defect regions onthe mask blank. By way of another example, the second characteristic ofthe cost function may include the pattern complexity of a design patternunder which a defect lies.

In one embodiment, the system 100 is configured to determine patterncomplexity by CD of patterns in the defect region and density ofsmall-CD patterns within the defect region. In another embodiment, thesystem 100 is configured to determine the exposed area of defects underan exposure region of the design pattern using the part of the defectthat is not covered by the absorber layer.

In step 906, one or more values indicative of the minimum of the costfunction are generated via a non-linear optimization procedure. In oneembodiment, the cost function is minimized by the non-linearoptimization procedure to determine one or more optimal rotation andtranslation parameters using the controller 108 of the system 100. Forexample, the cost function may be minimized using Bound Optimization BYQuadratic Approximation (BOBYQA) to determine the parameters of rotationand translation (as shown by Eqn. 2). For instance, the minimum of thecost function may indicate that a mask blank with a specific patternshould be rotated 90 degrees relative to the mask blank center andshifted approximately −1.1268 μm in the x-direction and 0.1956 μm in they-direction.

It is noted herein that any non-linear optimization procedure may beused. Therefore, the above description should not be construed aslimiting the scope of the present disclosure.

In step 908, one or more control signals are generated to adjust therotation and translation of the mask blank relative to the designpattern based on the one or more values determined in step 906. Forexample, as shown in FIG. 5, mask blank 500 may be rotated andtranslated a select amount based on the optimal rotation and translationparameters of the minimum of the cost function, such that the defects502 on the mask blank 500 do not lay under the exposure areas of adesign pattern 504 (e.g., are hidden by the absorber layer).

In step 910, the mask is generated with the adjusted design pattern toperform photolithography of a sample. For example, the mask generatedmay be an EUV photomask to be used by an EUV lithography sub-system(such as the EUV lithography sub-system 102 shown in FIGS. 1B-1C).

FIG. 10 illustrates a flowchart of an additional/alternative method 1000for reducing printable defects in EUV photomasks using a cost function,in accordance with one or more embodiments of the present disclosure. Itis noted herein that the steps of method 1000 may be implemented all orin part by system 100. It is further recognized, however, that themethod 1000 is not limited to the system 100 in that additional oralternative system-level embodiments may carry out all or part of thesteps of method 1000.

In step 1002, blank inspection of the mask blank 500 is performed togenerate a defect map. In one embodiment, the system 100 is configuredto direct the characterization sub-system 106 to generate a defect mapof a layer of the mask blank 500. For example, the characterizationsub-system 106 may be configured to identify the number of defects,their size, type, and location in the mask blank 500.

In step 1004, a cost function is generated with rotation and translationas parameters. In one embodiment, the controller 108 of the system 100is configured to generate a cost function based on a firstcharacteristic and a second characteristic of the cost function (such asthe cost function shown by Eqn. 1). For example, the firstcharacteristic of the cost function may include an exposed area ofdefect regions on the mask blank. By way of another example, the secondcharacteristic of the cost function may include pattern complexity of adesign pattern within a defect region.

In step 1006, one or more values indicative of the minimum of the costfunction are generated via a non-linear optimization procedure. In oneembodiment, the cost function is minimized by the non-linearoptimization procedure to find the parameters of rotation andtranslation. For example, the cost function may be minimized using BoundOptimization BY Quadratic Approximation (BOBYQA) to determine theoptimal parameters of rotation and translation. It is noted herein thatany non-linear optimization procedure may be used. Therefore, the abovedescription should not be construed as limiting the scope of the presentdisclosure.

In step 1008, one or more metrics indicative of how good the adjustedmask blank is for a specific design pattern are generated. For example,the controller 108 of the system 100 may be configured to generate oneor more metrics indicative of how good the mask blank is for the designpattern using Eqns. 3-4, described previously herein. In one embodiment,the one or more metrics include a score between 0 and 1. For example,the controller 108 of the system 100 may be configured to determine ascore between 0 and 1 using Eqns. 3-4. A score closer to 1 indicatesthat the adjusted mask blank with the design pattern is more likely tomitigate the one or more defects on the mask blank. For example, a scoreof 1 indicates that the adjusted mask blank with the design patternmitigates the one or more defects on the mask blank, while a score of 0indicates that the adjusted mask blank with the design pattern does notmitigate the one or more defects on the mask blank well. In this regard,the score gives a user an intuitive indication of how good the blank isfor the mask pattern P and how the pattern mask will effectively hideone or more of the defects in the blank.

In step 1010, one or more control signals are generated to adjust therotation and translation of the mask blank based on the estimatedparameters of the minimum of the cost function determined in step 1006or the one or more metrics indicative of how good the adjusted maskblank is for a specific pattern determined in step 1008. For example,the best mask blank from a mask blank library may be selected using theone or more metrics determined in step 1008, so that all mask blanks arebest utilized based on a specified pattern. For instance, the controller108 of the system 100 may be configured to obtain the highest score of0.9355 among mask blanks with a specific mask pattern after optimization(e.g., once the mask blank has been rotated 90 degrees with atranslation of −1.1268 μm in the x-direction and 0.1956 μm in they-direction). In this instance, the highest score indicates that themask blank is the best pair for the design pattern after the mask blankhas been rotated 90 degrees and translated −1.1268 μm in the x-directionand 0.1956 μm in the y-direction. Thus, it can maximally reduce blankwastage and greatly improve the yield in production environment.

In step 1012, the mask is generated with the adjusted mask blank toperform photolithography of a sample. For example, the mask generatedmay be an EUV photomask to be used by an EUV lithography sub-system(such as the lithography sub-system 102 shown in FIGS. 1B-1C).

All of the methods described herein may include storing results of oneor more steps of the method embodiments in memory. The results mayinclude any of the results described herein and may be stored in anymanner known in the art. The memory may include any memory describedherein or any other suitable storage medium known in the art. After theresults have been stored, the results can be accessed in the memory andused by any of the method or system embodiments described herein,formatted for display to a user, used by another software module,method, or system, and the like. Furthermore, the results may be stored“permanently,” “semi-permanently,” temporarily,” or for some period oftime. For example, the memory may be random access memory (RAM), and theresults may not necessarily persist indefinitely in the memory.

It is further contemplated that each of the embodiments of the methoddescribed above may include any other step(s) of any other method(s)described herein. In addition, each of the embodiments of the methoddescribed above may be performed by any of the systems described herein.

One skilled in the art will recognize that the herein describedcomponents operations, devices, objects, and the discussion accompanyingthem are used as examples for the sake of conceptual clarity and thatvarious configuration modifications are contemplated. Consequently, asused herein, the specific exemplars set forth and the accompanyingdiscussion are intended to be representative of their more generalclasses. In general, use of any specific exemplar is intended to berepresentative of its class, and the non-inclusion of specificcomponents, operations, devices, and objects should not be taken aslimiting.

As used herein, directional terms such as “top,” “bottom,” “over,”“under,” “upper,” “upward,” “lower,” “down,” and “downward” are intendedto provide relative positions for purposes of description, and are notintended to designate an absolute frame of reference. Variousmodifications to the described embodiments will be apparent to thosewith skill in the art, and the general principles defined herein may beapplied to other embodiments.

With respect to the use of substantially any plural and/or singularterms herein, those having skill in the art can translate from theplural to the singular and/or from the singular to the plural as isappropriate to the context and/or application. The varioussingular/plural permutations are not expressly set forth herein for sakeof clarity.

The herein described subject matter sometimes illustrates differentcomponents contained within, or connected with, other components. It isto be understood that such depicted architectures are merely exemplary,and that in fact many other architectures can be implemented whichachieve the same functionality. In a conceptual sense, any arrangementof components to achieve the same functionality is effectively“associated” such that the desired functionality is achieved. Hence, anytwo components herein combined to achieve a particular functionality canbe seen as “associated with” each other such that the desiredfunctionality is achieved, irrespective of architectures or intermedialcomponents. Likewise, any two components so associated can also beviewed as being “connected,” or “coupled,” to each other to achieve thedesired functionality, and any two components capable of being soassociated can also be viewed as being “couplable,” to each other toachieve the desired functionality. Specific examples of couplableinclude but are not limited to physically mateable and/or physicallyinteracting components and/or wirelessly interactable and/or wirelesslyinteracting components and/or logically interacting and/or logicallyinteractable components.

Furthermore, it is to be understood that the invention is defined by theappended claims. It will be understood by those within the art that, ingeneral, terms used herein, and especially in the appended claims (e.g.,bodies of the appended claims) are generally intended as “open” terms(e.g., the term “including” should be interpreted as “including but notlimited to,” the term “having” should be interpreted as “having atleast,” the term “includes” should be interpreted as “includes but isnot limited to,” and the like). It will be further understood by thosewithin the art that if a specific number of an introduced claimrecitation is intended, such an intent will be explicitly recited in theclaim, and in the absence of such recitation no such intent is present.For example, as an aid to understanding, the following appended claimsmay contain usage of the introductory phrases “at least one” and “one ormore” to introduce claim recitations. However, the use of such phrasesshould not be construed to imply that the introduction of a claimrecitation by the indefinite articles “a” or “an” limits any particularclaim containing such introduced claim recitation to inventionscontaining only one such recitation, even when the same claim includesthe introductory phrases “one or more” or “at least one” and indefinitearticles such as “a” or “an” (e.g., “a” and/or “an” should typically beinterpreted to mean “at least one” or “one or more”); the same holdstrue for the use of definite articles used to introduce claimrecitations. In addition, even if a specific number of an introducedclaim recitation is explicitly recited, those skilled in the art willrecognize that such recitation should typically be interpreted to meanat least the recited number (e.g., the bare recitation of “tworecitations,” without other modifiers, typically means at least tworecitations, or two or more recitations). Furthermore, in thoseinstances where a convention analogous to “at least one of A, B, and C,and the like” is used, in general such a construction is intended in thesense one having skill in the art would understand the convention (e.g.,“a system having at least one of A, B, and C” would include but not belimited to systems that have A alone, B alone, C alone, A and Btogether, A and C together, B and C together, and/or A, B, and Ctogether, and the like). In those instances where a convention analogousto “at least one of A, B, or C, and the like” is used, in general such aconstruction is intended in the sense one having skill in the art wouldunderstand the convention (e.g., “a system having at least one of A, B,or C” would include but not be limited to systems that have A alone, Balone, C alone, A and B together, A and C together, B and C together,and/or A, B, and C together, and the like). It will be furtherunderstood by those within the art that virtually any disjunctive wordand/or phrase presenting two or more alternative terms, whether in thedescription, claims, or drawings, should be understood to contemplatethe possibilities of including one of the terms, either of the terms, orboth terms. For example, the phrase “A or B” will be understood toinclude the possibilities of “A” or “B” or “A and B.”

It is believed that the present disclosure and many of its attendantadvantages will be understood by the foregoing description, and it willbe apparent that various changes may be made in the form, constructionand arrangement of the components without departing from the disclosedsubject matter or without sacrificing all of its material advantages.The form described is merely explanatory, and it is the intention of thefollowing claims to encompass and include such changes. Furthermore, itis to be understood that the invention is defined by the appendedclaims.

What is claimed:
 1. A system for reducing printable defects on a patternmask, comprising: a controller configured to be communicatively coupledto a characterization sub-system, wherein the controller includes one ormore processors configured to execute program instructions causing theone or more processors to: direct the characterization sub-system toperform inspection of a mask blank to generate a defect map of one ormore defects in the mask blank; generate a cost function based on afirst characteristic and a second characteristic, wherein the firstcharacteristic comprises an area of defect exposure of the one or moredefects on the mask blank, wherein the second characteristic comprisespattern complexity of a design pattern within a defect region; determineone or more values indicative of a minimum of the cost function via anon-linear optimization procedure; and generate one or more controlsignals to adjust rotation and translation of the mask blank relative tothe design pattern based on the determined one or more values indicativeof the minimum of the cost function.
 2. The system of claim 1, whereinthe controller is further configured to: determine one or more metricsindicative of how good the adjusted mask blank is for the designpattern.
 3. The system of claim 2, wherein the one or more metricsincludes a score between 0 and 1, wherein a score closer to 1 indicatesthat the adjusted mask blank with the design pattern is more likely tomitigate the one or more defects on the mask blank.
 4. The system ofclaim 1, wherein the controller is further configured to: add a marginto the size of the one or more defects in the mask blank, wherein theaddition of the margin is configured to position the one or more defectsa select distance from one or more edges of the design pattern.
 5. Thesystem of claim 1, wherein the rotation and translation of the maskblank is further configured to avoid placing the one or more defects onthe mask blank under design patterns of high complexity.
 6. The systemof claim 1, wherein the pattern complexity of the design pattern isdetermined by pattern critical dimension in the defect region of the oneor more defects on the mask blank and density of small-criticaldimension patterns in the defect region of the one or more defects onthe mask blank.
 7. The system of claim 1, wherein the area of defectexposure of the one or more defects on the mask blank is determinedusing an overlapping area of one or more defect regions with exposureregions of the design pattern.
 8. The system of claim 1, wherein thenon-linear optimization procedure includes Bound Optimization BYQuadratic Approximation (BOBYQA).
 9. The system of claim 1, wherein themask blank includes an extreme ultraviolet blank mask.
 10. The system ofclaim 1, wherein the design pattern is printed on the adjusted maskblank to generate the pattern mask, wherein the pattern mask includes anextreme ultraviolet pattern mask including a multilayer reflectorportion and an absorber layer.
 11. A system for reducing printabledefects on a pattern mask, comprising: a controller configured to becommunicatively coupled to a characterization sub-system, wherein thecontroller includes one or more processors configured to execute programinstructions causing the one or more processors to: direct thecharacterization sub-system to perform inspection of a mask blank togenerate a defect map of one or more defects in the mask blank; generatea cost function based on a first characteristic and a secondcharacteristic, wherein the first characteristic comprises an area ofdefect exposure of the one or more defects on the mask blank, whereinthe second characteristic comprises pattern complexity of a designpattern within a defect region; determine one or more values indicativeof a minimum of the cost function via a non-linear optimizationprocedure; determine one or more metrics indicative of how good the maskblank is for the design pattern; and generate one or more controlsignals to adjust rotation and translation of the mask blank relative tothe design pattern based on at least one of the determined one or morevalues indicative of the minimum of the cost function or the one or moremetrics indicative of how good the mask blank is for the design pattern.12. The system of claim 11, wherein the one or more metrics includes ascore between 0 and 1, wherein a score closer to 1 indicates that theadjusted mask blank with the design pattern is more likely to mitigatethe one or more defects on the mask blank.
 13. The system of claim 11,wherein the controller is further configured to: add a margin to thesize of the one or more defects in the mask blank, wherein the additionof the margin is configured to position the one or more defects a selectdistance from one or more edges of the design pattern.
 14. The system ofclaim 11, wherein the rotation and translation of the mask blank isfurther configured to avoid placing the one or more defects on the maskblank under design patterns of high complexity.
 15. The system of claim11, wherein the pattern complexity of the design pattern is determinedby pattern critical dimension in the defect region of the one or moredefects on the mask blank and density of small-critical dimensionpatterns in the defect region of the one or more defects on the maskblank.
 16. The system of claim 11, wherein the area of defect exposureof the one or more defects on the mask blank is determined using anoverlapping area of one or more defect regions with exposure regions ofthe design pattern.
 17. The system of claim 11, wherein the non-linearoptimization procedure includes Bound Optimization BY QuadraticApproximation (BOBYQA).
 18. The system of claim 11, wherein the maskblank includes an extreme ultraviolet blank mask.
 19. The system ofclaim 11, wherein the design pattern is printed on the adjusted maskblank to generate the pattern mask, wherein the pattern mask includes anextreme ultraviolet pattern mask including a multilayer reflectorportion and an absorber layer.
 20. A method for reducing printabledefects on a pattern mask, comprising: directing a characterizationsub-system to perform inspection of a mask blank to generate a defectmap of one or more defects in the mask blank; generating a cost functionbased on a first characteristic and a second characteristic, wherein thefirst characteristic comprises an area of defect exposure of the one ormore defects on the mask blank, wherein the second characteristiccomprises pattern complexity of a design pattern within a defect region;determining one or more values indicative of a minimum of the costfunction via a non-linear optimization procedure; and generating one ormore control signals to adjust rotation and translation of the maskblank relative to the design pattern based the determined one or morevalues indicative of the minimum of the cost function.
 21. The method ofclaim 20, wherein the method further comprises: determining one or moremetrics indicative of how good the adjusted mask blank is for the designpattern.
 22. The method of claim 21, wherein the one or more metricsincludes a score between 0 and 1, wherein a score closer to 1 indicatesthat the adjusted mask blank with the design pattern is more likely tomitigate the one or more defects on the mask blank.
 23. The method ofclaim 20, wherein the method further comprises: adding a margin to thesize of the one or more defects in the mask blank, wherein the additionof the margin is configured to position the one or more defects a selectdistance from one or more edges of the design pattern.
 24. The method ofclaim 20, wherein the rotation and translation of the mask blank isfurther configured to avoid placing the one or more defects on the maskblank under design patterns of high complexity.
 25. The method of claim20, wherein the pattern complexity of the design pattern is determinedby pattern critical dimension in the defect region of the one or moredefects on the mask blank and density of small critical dimensionpatterns in the defect region of the one or more defects on the maskblank.
 26. The method of claim 20, wherein the area of defect exposureof the one or more defects on the mask blank is determined using anaccumulated overlapping area of one or more defect regions with exposureregions of the design pattern.
 27. The method of claim 20, wherein thenon-linear optimization procedure includes Bound Optimization BYQuadratic Approximation (BOBYQA).
 28. The method of claim 20, whereinthe mask blank includes an extreme ultraviolet blank mask.
 29. Themethod of claim 20, wherein the design pattern is printed on theadjusted mask blank to generate the pattern mask, wherein the patternmask includes an extreme ultraviolet pattern mask including a multilayerreflector portion and an absorber layer.
 30. A method for reducingprintable defects on a pattern mask, comprising: performing inspectionof a mask blank to generate a defect map of one or more defects on themask blank using a characterization sub-system; generating a costfunction based on a first characteristic and a second characteristic,wherein the first characteristic comprises an area of defect exposure ofthe one or more defects on the mask blank, wherein the secondcharacteristic comprises pattern complexity of a design pattern within adefect region; determining one or more values indicative of a minimum ofthe cost function via a non-linear optimization procedure; determiningone or more metrics indicative of how good the mask blank is for thedesign pattern; and generating one or more control signals to adjustrotation and translation of the mask blank relative to the designpattern based on at least one of the determined one or more valuesindicative of the minimum of the cost function or the one or moremetrics indicative of how good the mask blank is for the design pattern.31. The method of claim 30, wherein the one or more metrics includes ascore between 0 and 1, wherein a score closer to 1 indicates that theadjusted mask with the design pattern is more likely to mitigate the oneor more defects in the mask blank.
 32. The method of claim 30, whereinthe method further comprises: adding a margin to the size of the one ormore defects in the mask blank, wherein the addition of the margin isconfigured to position the one or more defects a select distance fromone or more edges of the design pattern.
 33. The method of claim 30,wherein the rotation and translation of the mask blank is furtherconfigured to avoid placing the one or more defects on the mask blankunder design patterns of high complexity.
 34. The method of claim 30,wherein the pattern complexity of the design pattern is determined bypattern critical dimension in the defect region of the one or moredefects on the mask blank and density of small-critical dimensionpatterns in the defect region of the one or more defects on the maskblank.
 35. The method of claim 30, wherein the area of defect exposureof the one or more defects on the mask blank is determined using anaccumulated overlapping area of one or more defect regions with exposureregions of the design pattern.
 36. The method of claim 30, wherein thenon-linear optimization procedure includes Bound Optimization BYQuadratic Approximation (BOBYQA).
 37. The method of claim 30, whereinthe mask blank includes an extreme ultraviolet blank mask.
 38. Themethod of claim 30, wherein the design pattern is printed on theadjusted mask blank to generate the pattern mask, wherein the patternmask includes an extreme ultraviolet pattern mask including a multilayerreflector portion and an absorber layer.